This paper presents an effective semi-analytical approach for predicting lower-order dynamics of a five degrees-of-freedom (DOF) hybrid robot named TriMule, which is composed of a 3-DOF parallel mechanism plus a 2-DOF A/C wrist. In this method, the governing equations of motion of limbs within the parallel mechanism are first formulated by finite element analysis (FEA) and then reduced to super-element models. This is followed by exploiting a general stiffness model of multiple DOF joints connecting the super-elements. These two threads lead to the reduced dynamic model of the parallel mechanism while keeping the full set of lower-order modes retained. Finally, the dynamic model of entire system is established by merging the models of parallel mechanism and wrist. The computational results show that the lower-order natural frequencies, mode shapes of the entire system, and the frequency response functions (FRFs) of the robot tool center point (TCP) estimated by the proposed approach have very good agreement with those obtained by a full order FE model and experimental modal tests. The merits of this approach lie in that the established model allows the full set of lower-order dynamics of the entire system to be predicted effectively and accurately by only using fourteen generalized coordinates.

本文提出了一种有效的半分析方法，用于预测名为TriMule的五自由度（DOF）混合机器人的低阶动力学，该机器人由3-DOF并联机构和2-DOF A / C手腕组成。在这种方法中，首先通过有限元分析（FEA）来建立并联机构中肢体运动的控制方程，然后将其简化为超单元模型。然后，利用连接超元素的多个自由度接头的一般刚度模型。这两个线程导致并行机制的动态模型减少，同时保留了完整的低阶模式集。最后，通过将并联机构和腕部模型合并，建立了整个系统的动力学模型。计算结果表明，低阶固有频率 整个系统的模态形状以及通过所提出的方法估算的机器人工具中心点（TCP）的频率响应函数（FRF）与通过全阶有限元模型和实验模态测试获得的结果非常吻合。该方法的优点在于，所建立的模型仅通过使用14个广义坐标就可以有效，准确地预测整个系统的所有低阶动力学。